Updates for today. You all can enjoy my newest analysis.
Thanks LoyceV for updates last two weeks.
I am busy recent days, so I did not update my topic last week.
I will do it hours later today.
Abstract (for truncated dataset)
50% of observed days (since 19/02/2018 to 02/12/2018) have its total daily merits below 626 (the median) or higher than 626.
Importantly,
50% of observed days have their total daily merits in the range from 521 to 774, which is the interquartile range that ranges from the 25th quartile (Q1) to the 75th quartile (Q3).
The minimum and maximum daily merits during the period are 347 and 2463, respectively.
Potential outliers are days that have total merits above 1154 or below 142.About medians of merits over days of week, Monday is the highest with 674 merits distributed on Mondays in medians, and Friday is the lowest with the median of Friday merits is 542.
There are nearly 24% difference between the medians of Friday and Monday.And, Friday is the only day of week which has median lower than 600.
Updates:1) Daily merits1.1. Full dataset (from 24/1/2018 to 2/12/2018)
I dropped days after 2/12/2018 because those days belong to the 2018w49, which has not completed with LoyceV data source).
Now, lets' take a look at its basic statistics:
During the whole period since the beginning day of merit system, the daily merits
has its median is 643, which means that 50% of those observed days have their daily merits above 643, and 50% of them have their daily merits above 643.
- The interquartile range (from 25th to 75th quartile): is 530 - 858. It means that 50% of those observed days have daily merits in the range from 530 to 858. In addition, 25% of those days have daily merits below 530 (below the 25h quartile), while 25% of them have daily merits above 858 (above the 75th quartile).
- The mean +/- standard deviation: is 880 +/- 952. I don't want to use those statistics due to dramatical biases from outliers.
Extremely potential outliers are days have their total daily merits above 1350 or below 38. Detailed calculations presented below:
- Below: Q1 -1.5*IQR = 530-(1.5*328) = 38;
- or Above: Q3 + 1.5*IQR = 858+(1.5*328) = 1350.
- IQR = Q3 - Q1 = 858 - 530 = 328
From now on, I only presented analytical results for truncated dataset.
What is truncated dataset?
It is the dataset, after truncating / dropping all days before 19/02/2018, which are extremely outliers.
. list id date week month merit if merit > 1350 & merit != .
+--------------------------------------------+
| id date week month merit |
|--------------------------------------------|
1. | 1 24jan2018 2018w4 2018m1 13018 |
2. | 2 25jan2018 2018w4 2018m1 6761 |
3. | 3 26jan2018 2018w4 2018m1 4493 |
4. | 4 27jan2018 2018w4 2018m1 3489 |
5. | 5 28jan2018 2018w4 2018m1 3188 |
|--------------------------------------------|
6. | 6 29jan2018 2018w5 2018m1 3799 |
7. | 7 30jan2018 2018w5 2018m1 4192 |
8. | 8 31jan2018 2018w5 2018m1 2820 |
9. | 9 01feb2018 2018w5 2018m2 2545 |
10. | 10 02feb2018 2018w5 2018m2 2568 |
|--------------------------------------------|
11. | 11 03feb2018 2018w5 2018m2 1867 |
12. | 12 04feb2018 2018w5 2018m2 2167 |
13. | 13 05feb2018 2018w6 2018m2 2077 |
14. | 14 06feb2018 2018w6 2018m2 2308 |
15. | 15 07feb2018 2018w6 2018m2 2141 |
|--------------------------------------------|
16. | 16 08feb2018 2018w6 2018m2 2141 |
17. | 17 09feb2018 2018w6 2018m2 1448 |
18. | 18 10feb2018 2018w6 2018m2 1747 |
19. | 19 11feb2018 2018w6 2018m2 1442 |
21. | 21 13feb2018 2018w7 2018m2 1579 |
|--------------------------------------------|
22. | 22 14feb2018 2018w7 2018m2 2513 |
23. | 23 15feb2018 2018w7 2018m2 1991 |
24. | 24 16feb2018 2018w7 2018m2 1411 |
25. | 25 17feb2018 2018w7 2018m2 1608 |
27. | 27 19feb2018 2018w8 2018m2 1403 |
|--------------------------------------------|
32. | 32 24feb2018 2018w8 2018m2 1409 |
34. | 34 26feb2018 2018w9 2018m2 1382 |
38. | 38 02mar2018 2018w9 2018m3 1696 |
48. | 48 12mar2018 2018w11 2018m3 1354 |
236. | 236 16sep2018 2018w37 2018m9 2463 |
|--------------------------------------------|
237. | 237 17sep2018 2018w38 2018m9 1862 |
+--------------------------------------------+
As you can easily see that there are some days listed as extremely outliers after 19th Feb. 2018, but I left them in the dataset, not truncated them, in order to have full weeks in truncated dataset.
- Median: 626
- Interquartile range: 521 - 774
- Mean +/- standard deviation: 695 +/- 268
- Extremely potential outliers: above 1154 or below 142.
With IQR = 774 - 521 = 253
Q1 - 1.5*IQR = 521 - 1.5*253 = 141.5 ~ 142
Q3 + 1.5*IQR = 774 + 1.5*253 = 1153.5 ~ 1154.
Box plotsa) Box plot of daily merits since 19th February 2018 to 2nd December 2018.Merit after presents statistics of the whole period from 19/2/2018 to 2/12/2018.
w26 presents statistics of the period that started on 19/2/2018 to the end of the week26 (on 01/7/2018)
b) Box plot of daily merit (full dataset). This one is only for reference.
Merits over days of weekRaw statisticsSummary for variables: merit
by categories of: dofw
dofw | N mean sd p50 p25 p75 min max
----------+--------------------------------------------------------------------------------
Sunday | 41.0 715.7 360.5 603.0 476.0 829.0 412.0 2463.0
Monday | 41.0 771.3 314.1 674.0 562.0 884.0 455.0 1862.0
Tuesday | 41.0 715.0 246.1 632.0 580.0 767.0 383.0 1326.0
Wednesday | 41.0 723.5 227.1 652.0 562.0 761.0 435.0 1268.0
Thursday | 41.0 687.0 220.7 644.0 528.0 774.0 376.0 1333.0
Friday | 41.0 611.7 238.0 542.0 463.0 698.0 348.0 1696.0
Saturday | 41.0 639.5 223.3 614.0 463.0 688.0 347.0 1409.0
----------+--------------------------------------------------------------------------------
Total | 287.0 694.8 268.1 626.0 521.0 774.0 347.0 2463.0
-------------------------------------------------------------------------------------------
What we got here?
The days of week that have lowest and highest
means of totally merits are Friday and Wednesday, at 612 and 724 merits distributed, respectively.
It means there are (724 - 612) = 212 merit difference or
the Wednesday have nearly 18% total merits higher than the Friday. Personally, it is a dramatical difference.
. di (724-612)*100/612
18.300654
Now, how about
median difference?
The days of week that have lowest and highest
medians of totally merits are Friday and Monday, at 542 and 674, respectively.
It means that there are (674-542) = 132 merit points diference between the Friday and Monday.
In other words, there are
nearly 24% difference between the medians of Friday and Monday.. di (674-542)*100/542
24.354244
Box plots:a) Outliers displayed.
b) Outliers non-displayed.
Statistics of full dataset (just for reference)
Summary for variables: merit
by categories of: dofw
dofw | N mean sd p50 p25 p75 min max
----------+--------------------------------------------------------------------------------
Sunday | 45.0 831.8 557.3 619.0 486.0 880.0 412.0 3188.0
Monday | 44.0 882.5 582.4 681.0 575.5 945.0 455.0 3799.0
Tuesday | 44.0 849.9 628.7 638.5 580.0 890.5 383.0 4192.0
Wednesday | 45.0 1114.5 1882.6 681.0 569.0 963.0 435.0 13018.0
Thursday | 45.0 924.5 995.1 673.0 530.0 846.0 376.0 6761.0
Friday | 45.0 777.7 695.0 554.0 475.0 774.0 348.0 4493.0
Saturday | 45.0 776.2 542.4 627.0 506.0 778.0 347.0 3489.0
----------+--------------------------------------------------------------------------------
Total | 313.0 879.7 951.8 643.0 530.0 858.0 347.0 13018.0
-------------------------------------------------------------------------------------------